Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16840657 | C2 | semidirect |
| 2. C2×#16840636 | C2 | semidirect |
| 3. #21460805 | C2 | direct (N × H) |
| 8. #16840657 | C22 | semidirect |
| 10. #16840636 | C22 | semidirect |
| 15. #16839995 | C4 | semidirect |
| 17. C2×#14519711 | C4 | semidirect |
| 19. C22×D8×C61 | C4 | semidirect |
| 42. #14519711 | C2×C4 | semidirect |
| 48. C2×D8×C61 | C2×C4 | semidirect |
| 163. C2×C61 | #1347 | semidirect |
| 170. C22×D8 | #6923 | semidirect |
| 185. C61 | C2×#1347 | semidirect |
| 192. C2×D8 | C2×#6923 | semidirect |
| 327. C2 | #21460805 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840657 | 2 |
| C2×#16840636 | 2 |
| #21460805 | 2 |
| C2×#16839995 | 2 |
| C2×#1347 | 61 |